Homeier was born in Chicago on October 5, 1930. He began to act for radio shows at the age of six as Skippy Homeier. Then, at the age of 11, he worked on the radio show Portia Faces Life, as well as making "dramatic commercial announcements" on The O'Neills and Against the Storm. In 1942, he also joined the casts of Wheatena Playhouse and We, the Abbotts. From 1943 until 1944, he played the role of Emil in the Broadway play, and film Tomorrow, the World!. Cast as a child indoctrinated into Nazism, who is brought to the United States from Germany following the death of his parents, Homeier was praised for his performance. He played the troubled youngster in the film adaptation of Tomorrow, the World! (1944) and received good reviews playing opposite Fredric March and Betty Field as his American uncle and aunt.

He also developed a talent for playing strong character roles in war films, such as Halls of Montezuma (1950), Sam Fuller's Fixed Bayonets (1951) and Beachhead (1954).

In 1954, he guest-starred in an episode of the NBC legal drama Justice, based on cases of the Legal Aid Society of New York. He was cast later in an episode of Steve McQueen's Wanted Dead or Alive, a CBS western series. Homeier played a man sought for a crime of which he is innocent, but who has no faith in the legal system's ability to provide justice. Fleeing from McQueen's bounty hunter character Josh Randall, Homeier's character foot slipped. He accidentally fell to his death from a cliff.

Homeier appeared as Kading in an episode of the NBC western Jefferson Drum ("The Post", 1958), starring Jeff Richards. Then, from 1960 to 1961, he starred in the title role in Dan Raven, a crime drama also on NBC set on Sunset Strip of West Hollywood, California, with a number of celebrities playing themselves in guest roles. The series only lasted for 13 episodes. In the summer of 1961, he appeared in an episode of The Asphalt Jungle, and later that same year he performed as a replacement drover and temporary "ramrod" in an episode of Rawhide ("Incident of the Long Shakedown"). Homeier also made two guest appearances on Perry Mason, both times as the defendant. In 1961, he played Dr. Edley in "The Case of the Pathetic Patient", and in 1965 he played the police sergeant Dave Wolfe in "The Case of the Silent Six". In 1964, he guest-starred in The Addams Family episode "Halloween With The Addams Family" with Don Rickles. Also in 1964, he portrayed the Dr. Clinton role in The Outer Limits episode "Expanding Human".

Homeier was cast in the feature film The Ghost and Mr. Chicken (1966) with Don Knotts; and he continued to be frequently cast on television as a guest star, often as a villain, including in all four of Irwin Allen's science-fiction series in the mid-to-late 1960s. He guest-starred as well on Star Trek: The Original Series in two episodes: as the Nazi-like character Melakon in "Patterns of Force" (1968), and as Dr. Sevrin in "The Way to Eden" (1969). One of his last roles was a one-liner in the television film The Wild Wild West Revisited (1979) as a senior Secret Service official. He retired from acting aged 50.

Homeier died on June 25, 2017 at the age of 86 from spinal myelopathy at his home in Indian Wells, California. He is survived by his wife, Della, and Homeier's sons Peter and Michael from his first marriage (1951-1962) to Nancy Van Noorden Field.